So by your definition you are saying all the foreign nationals who fought in the United States Army in Iraq, Afghanistan, Syria, Grenada, Vietnam, Korea, World War II, World War I, Spanish American War, Civil War, Mexican War, Seminole War, War of 1812, Quasi War with France and the American Revolution were mercenaries. Currently you must be a permanent legal resident of the US to join our military but that is a relatively new condition of enlistment.
Americans enlisted in foreign militaries to fight in WW1 and WW2 for ideological reasons which by any reasonable definition excludes them from being labled mercenaries. Getting paid or not is irrelevant. A lack of ideological commitment to the government or cause you are being paid to serve is a key element of being a mercenary. A mercenary also generally needs to be a professional soldier or military expert as a primary mode of employment.
The definition you used in your example is incredibly broad and not something that has been accepted in this country or most of the world for hundreds of years.
Don’t make it rocket science logic, it is not. Your first mistake is thinking “ mercenary “ is bad or derogatory. It is not.
The definition is simple. The connotations are broad.
If you are a citizen of one country, and go to fight in hostilities for a foreign country who pays you to use your skills, you are a mercenary. Very easy to understand.
The ammo truck driver, the medic, the aircraft mechanic, the pilot, the computer nerd, the force protection specialist, the SARS guy, etc…